Re: not absorbing iodine?
In an odd coincidence, I was just listening to Byron Richards' weekly podcast, and he answered a woman's question that sounded a lot like yours. Prone to heat exhaustion, doesn't sweat much, and anxiety symptoms. He suggested that she was having low blood sugar symptoms when her liver wasn't able to prop up her blood sugar. This gave the anxiety. Sympathetic nerve signals are sent out to break down protein around the body to provide the blood sugar, and the ramping up of the sympathetic nervous system gives the red face and flushing, and maybe a poundy heart. Weak adrenals were causing an electrolyte imbalance, which contributed to the not sweating.
The solution was to increase adrenal gland nutrition. Most important was to have a high amount of protein at breakfast, though he recommended protein and some fat at all three meals. B vitamins, especially pantethine 300-600 mg at breakfast and lunch; vit C 3-4 g, magnesium, and potassium. (I wouldn't be able to handle the potassium, and instead rely on heavily salted water.) He said once she stabilized the ability of her adrenals to synthesize hormones, she shouldn't have the erratic symptoms.
Something to think about, perhaps. And yes, iodine helps the health of all your hormone-producing glands.
If you'd like to listen for yourself, the podcast (dated 4/21/10) is available until next Wednesday when he posts another podcast. This question was about 27 minutes in. Don't let it throw you that he tied the problem to the woman's menstrual cycles -- it's still about her adrenal glands! :)
http://www.wellnessresources.com/podcast/#podcast